OFFSET
1,1
COMMENTS
If 2n-1 is a provable Riesel number (A101036), then there exists a finite set of primes P(2n-1) such that every 2^x-(2n-1) > 0 is divisible by p(x) in P(2n-1). If some 2^x-(2n-1) = p(x), then a(n) = p(x). Otherwise, p(x) is a proper divisor of 2^x-(2n-1), which must be composite, and no a(n) exists.
For example, if n = 254602, then 2n-1 = 509203 is a provable Riesel number. Every 2^x-509203 > 0 is divisible by prime p(x) in P(509203) = {3,5,7,13,17,241}. 2^x-509203 > 0 implies x >= 19 implies 2^x-509203 > 241 >= p(x), so p(x) is a proper divisor and every 2^x-509203 is composite. Hence a(254602) does not exist.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..935
EXAMPLE
a(1) = 3 is the first Mersenne prime;
a(64) = 2^47 - 127 = 140737488355201, where 47 = A096502(64), 127 = 2*64 - 1.
MATHEMATICA
f[n_]:=Module[{lst={}, exp=Ceiling[Log[2, 1+n]]}, While[!PrimeQ[2^exp-n], exp++]; AppendTo[lst, 2^exp-n]]; Flatten[f/@Range[1, 1001, 2]] (* Ivan N. Ianakiev, Mar 08 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 13 2004
STATUS
approved